Barebones, classic car challenge

I have a 1964 Ford Falcon with an AM mono radio, one speaker. Because it is an old car, you car practically crawl into the dashboard- it is all open. I want install a little amplifier so that I can hook my portable MP3 player in.

Any off the shelf product would be severe overkill, and ruin the look and feel of the car. I want to get something simple so that I can hide everything within the dashboard, with just a cord coming out to a player I would plug in (then hide back in the dash).

I am happy to roll up my sleeves and sweat through installation, if I knew what type of amp would work. Asking most car stereo guys makes them shake, as they stifle their laughter.

Key questions are- what is the right amount of amps for one ancient dashboard speaker, and how to I hook it to the battery. If I splice the cords with regular car stereo cords, would that work ok?